A note on costs minimization with stochastic target constraints

Yan Dolinsky, Benjamin Gottesman, Ori Gurel-Gurevich

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1 Scopus citations

Abstract

We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi-linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.

Original languageAmerican English
Article number11
JournalElectronic Communications in Probability
Volume25
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020, Institute of Mathematical Statistics. All rights reserved.

Keywords

  • Backward stochastic differential equations
  • Optimal stochastic control

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